Proof by Induction
Created | Updated Apr 1, 2002
Foreword: Induction techniques are very popular, even the Army uses them.
It's a myth that in southern
hemispheres of any world the other way 'round is also true.
Description: Proof by induction is used on equations with n in them.
Sample: Proof of induction without proof of induction
We know it's true for n equal to 1. Now assume that it's
true for every natural number less than n. N is arbitrary,
so we can take n as large as we want.
If n is sufficiently large, the case of n+1 is trivially
equivalent, so the only important n are n less than n.
We can take n=n (from above), so it's true for n+1 because it's
just about n.
QED. (QED translates from the Latin as "So what?")
It's a myth that in southern
hemispheres of any world the other way 'round is also true.
Description: Proof by induction is used on equations with n in them.
Sample: Proof of induction without proof of induction
We know it's true for n equal to 1. Now assume that it's
true for every natural number less than n. N is arbitrary,
so we can take n as large as we want.
If n is sufficiently large, the case of n+1 is trivially
equivalent, so the only important n are n less than n.
We can take n=n (from above), so it's true for n+1 because it's
just about n.
QED. (QED translates from the Latin as "So what?")
